According to many scientists and clinicians, genomics is taking on a key role in the field of medicine. Impressive advances in genome sequencing have opened the way to a variety of revolutionary applications in modern healthcare. In particular, the increasing understanding of the human genome, and of its relation to diseases and response to treatments brings promise of improvements in better preventive and personalized medicine. However, this progress raises important privacy and ethical concerns that need to be addressed. Indeed, each genome is the ultimate identifier of its owner and, due to its nature, it contains highly personal and privacy-sensitive data. In this article, after summarizing recent advances in genomics, we discuss some important privacy issues associated with human genomic information and methods put in place to address them.